arXiv subjects

Barbora Barancikova

Publications and source records attributed to Barbora Barancikova.

3 recordsLinked to original sources

arXiv2026

Improving Function Space Flow Matching with Kernel Optimal Transport

Generative models for function-valued data, such as time series and solutions of partial differential equations, must learn distributions over infinite-dimensional spaces. Functional Flow Matching (FFM) extends Flow Matching to this setting, learning a velocity field whose flow transports a Gaussian prior to the data distribution, but it inherits the independent endpoint pairing of standard Flow Matching: in each batch, prior and data samples are matched arbitrarily, so the conditional bridge must traverse both the shared global structure of the dataset and instance-specific residuals. In function space this is harder to fix than in finite dimensions, since optimal transport (OT) on function spaces is delicate to formulate and a flat Euclidean surrogate ignores the geometry that distinguishes function-valued data. We propose kernel Functional Flow Matching (kFFM), which replaces the independent pairing by entropic OT under a kernel-induced cost, the coupling underlying the Hilbert Sinkhorn Divergence (HSD), leaving the FFM neural-operator architecture unchanged. We prove that the kernel cost and the HSD objective are uniformly bounded and well-posed on Banach ambient spaces, derive an error decomposition against quadratic-cost OT on compact metric spaces that isolates an irreducible kernel-cost mismatch term, and prove a discretization-invariance bound whose rate is governed by Sobolev regularity. Empirically, kFFM improves distributional matching over FFM, diffusion, adversarial, and finite-dimensional OT baselines on time-series and PDE benchmarks, with significant paired-seed gains over FFM and improvements that persist under non-kernel and physics-based diagnostics, including a turbulent Navier-Stokes benchmark. Bounded kernel costs already outperform raw $L^2$ Sinkhorn, and function-space-aware kernels (signature, Sobolev RBF) give further gains on rough or path-valued data.

cs.LG↗

arXiv2026

Stable and Near-Reversible Diffusion ODE Solvers for Image Editing

The inversion of diffusion models plays a central role in image editing. Algebraically reversible ODE solvers provide an appealing approach to diffusion inversion for text-guided image editing, by eliminating the inversion error inherent in DDIM-based editing pipelines. However, empirical results indicate that reversibility alone is insufficient. As edits require larger semantic or visual changes, reversible diffusion solvers often exhibit instabilities and suffer sharp drops in output quality. In this paper, we show that the trade-off between exact reversibility and numerical stability manifests empirically as a trade-off between background preservation and prompt alignment in image editing. We then investigate the use of near-reversible Runge-Kutta methods as a more stable alternative to exactly reversible diffusion schemes. When combined with a vector-field smoothing strategy, the resulting approach improves edit fidelity, remains stable under large edits, and largely retains the background-preservation benefits of reversible solvers.

cs.CV↗

arXiv2025

SigDiffusions: Score-Based Diffusion Models for Time Series via Log-Signature Embeddings

Score-based diffusion models have recently emerged as state-of-the-art generative models for a variety of data modalities. Nonetheless, it remains unclear how to adapt these models to generate long multivariate time series. Viewing a time series as the discretisation of an underlying continuous process, we introduce SigDiffusion, a novel diffusion model operating on log-signature embeddings of the data. The forward and backward processes gradually perturb and denoise log-signatures while preserving their algebraic structure. To recover a signal from its log-signature, we provide new closed-form inversion formulae expressing the coefficients obtained by expanding the signal in a given basis (e.g. Fourier or orthogonal polynomials) as explicit polynomial functions of the log-signature. Finally, we show that combining SigDiffusions with these inversion formulae results in high-quality long time series generation, competitive with the current state-of-the-art on various datasets of synthetic and real-world examples.

cs.LG↗